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Cook Dal: Pressure cook toor dal with 1.5 cups water, 1/4 tsp turmeric, and 2 drops oil for 4 whistles until soft. Mash smooth; set aside.
Roast Masala: Heat 1 tsp oil in a pan. Roast chana dal, coriander seeds, black peppercorns, and red chillies on medium-low until golden (2 mins). Add grated coconut; toast until light golden-brown (2 mins). Cool and grind with 3–4 tbsp water into a smooth paste.
Boil Karela: In a pot, combine sliced bitter gourd, tamarind juice, 1/2 cup water, 1/4 tsp turmeric, and salt. Boil over medium heat for 10–12 minutes until bitter gourd is fork-tender. Add boiled black chickpeas if using.
Combine & Simmer: Stir the ground coconut-spice paste and jaggery into the cooked gourd. Simmer for 3 minutes. Stir in the mashed toor dal plus 1/2 cup water. Simmer on low heat for 4–5 minutes until the gravy turns glossy and thick.
Temper: Heat 1 tbsp oil in a small pan. Splutter mustard seeds, then add urad dal, hing, and curry leaves. Pour over the hot pitlai. Cover for 5 minutes before serving.
Toast the coconut gently on low heat to develop a rich, nutty flavor without scorching.
If the final dish tastes too sharp or bitter, stir in an extra 1/2 teaspoon of jaggery and a splash of water, then simmer for 1 minute.
Use sesame oil (gingelly oil) for authentic South Indian flavor.